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# Mathematical Modeling of Steam Solenoid Valve

04/05/2012 2:38 AM

I need to develop a mathematical model for a steam solenoid valve such that the resulting transfer function has its input as Voltage/current, and the output as mass flow of steam.

I need to use this model for designing a control system.

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#1

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 3:17 AM

That's a bit oblique. What does this control system do?

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#2

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 3:52 AM

It is a temperature control system. the solenoid steam valve regulates the quantity of heat flow into the Plate Heat Exchanger by varying the mass flow rate of the steam flow. the input is voltage/current that it will receive from the PID controller to regulate the level of opening of the steam valve. the output will be mass flow rate of steam.

I know that a solenoid valve is an electromechanical device. the solenoid valve takes in current from the PID controller. the current energizes the solenoid which slides the valve positioner to allow a volume rate of steam to pass. This is what I want to model.

Thanks.

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#3

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 4:58 AM

It is usual to determine some feature of the process fluid that needs controlling, and not the utility fluid equipment. After all, the qualities of the utility fluid will vary with time depending on disturbances elsewhere in the utility fluid system, so a mass flowrate of x kg/h at one time might need +/- 15% at another time to achieve the same impact on the process fluid measured value.

For modelling, the behaviour of the utility fluid equipment can be swept up into a first-order transfer function with a time constant of, oh, say 1-5 seconds depending upon the size of the line from the utility fluid actuating element and the exchanger itself. This approximation may be sufficient to produce a credible model. The outcome of the model ought to be a first stab at the proportional, integral and derivative terms for the real-world controller, enabling a faster approach to tuning properly when the process goes live.

Does that help?

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#4

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 5:11 AM

Thanks, I get that point. can I get some mathematical expression for this?

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#6

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 1:55 PM

and what point did you get?

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#5

### Re: Mathematical Modeling of Steam Solenoid valve

04/05/2012 9:33 AM

Solenoid valves typically have on-off action - they are either fully on or fully off. PID controllers have variable action - the output is proportional to the desired final control device action. In many real-world applications, the PID controller would have a variable current of 4 to 20 mA, corresponding to a control valve position of fully closed to fully open.

Does your modeling software have a control valve device, not solenoid valve?

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#7

### Re: Mathematical Modeling of Steam Solenoid Valve

04/06/2012 3:30 AM

First you can simulate the valve as "on-off" device with some transportation delay, which may be represented at the first step as "0". By the way - the very useful programming instrument in this case is MATLAB/Simulink. All needed blocks for modelling are there. The second: a flow rate during valve is dependent from the pressure drop on this valve and a temperature of a steam. The appropriate expression may be found in an any course of hydraulics or pneumatic. Let say: Q = sqrt(P2 - P1) - the simplest form. You can determine inlet pressure P2 by the const independent value or by variable parameter (depending on your control system). The outlet pressure P2 has to be the function of the structure of the heat exchange and the principle of its activity. After the model will be created you can run simulation process and to observe the results.

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#8

### Re: Mathematical Modeling of Steam Solenoid Valve

04/16/2012 6:50 AM

1- you have to define your valve there are two basic principles: the "digital" which are either on or off and the "proportional" which can get an infinite number of positions between full off and full on. In all cases between a change in voltage and the change in aperture there is a delay determined by the electromagnetic actuator in the valve (its impedance) and the mechanical design (i.e. friction, spring rates, inertia aso)

2- the flow across the valve depends on the ratio between the 2 pressures (in front and behind) on this ratio depends the law for the mass flow: if the ratio p behind/p infront < critical threshold the flow is chocked and the equation mentioned above is not any more valid. It is valid only if above ratio > critical threshold.

As you see if you want to make a detailed model it is not as simple as it was suggested.

But do not be afraid the model can be simplified if you can estimate the time constants of process and valve. If the valve is very fast (on/off type) you can assume either a step function for its area or a ramp for the opening time as time basis.

For the proportional valve you can use a time delay and a linear term or a term 1st order (1-exp(-t/T)).

If the pressures are near to each other then the ratio is > the critical threshold which is around 0.5 and you can use the suggested equation.

As you see all depends on the relative value of parameters for the valve and the process.

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#9

### Re: Mathematical Modeling of Steam Solenoid Valve

04/16/2012 8:20 AM

The valve I want to model is for steam control. I didn't realise untill I got comments that solenoid valve is a 2-position valve. I will like you to shed more light on how i can model an electrically actuated control valve mathematically, maybe with an example. I wont mind if you have materials that can help me understand better. I intend making a simple model that relates steam flow output with controller electrical input.

Thanks

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#10

### Re: Mathematical Modeling of Steam Solenoid Valve

04/16/2012 4:11 PM

First of all you have to look at similar valves and get an information about their reaction time. Usually it is the time between the electric "on" and the moment the valve if full open. If the electric "on" is voltage then it takes a time till the magnetic force is big enough to start the opening stroke. This is due to time necessary to build up the magnetic field to the required intensity. Depending on the yoke design the magnetic force can evolute in different ways over the stroke. The simplest approximation is to consider a linear stroke/time growth. It is wrong but if the opening time is short it will not change results very much.

If the electric "on" is on current the problem is different and the stroke can be considered as a step.

What you have to model is the opening and what I wrote above gives you all informations you need.

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#11

### Re: Mathematical Modeling of Steam Solenoid Valve

04/17/2012 6:22 AM

another way to control your flow rate is to use a control valve pneumaticaly operated.These come with a current to pneumatic converter. Thus all you need is a supply from a controller of 4-20mA to the control valve. The signal will cause the valve to open or close since this value will be conveted to pressure. The controller will be getting its signal from a transducer ie RTD. so its RTD(tempreture)---controller(current)----valve(pressure)---- Diaphram which is the actuator.

I also need help on how i can simulate this with Matlab Simulink coz wat i need is a mathematical equation

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